Entangling ability of a beam splitter in the presence of temporal which-path information

We calculate the amount of polarization-entanglement induced by two-photon interference at a lossless beam splitter. Entanglement and its witness are quantified, respectively, by concurrence and the Bell-Clauser-Horne-Shimony-Holt (CHSH) parameter. In the presence of a Mandel dip, the interplay of two kinds of which-path information--temporal and polarization--gives rise to the existence of entangled polarization states that cannot violate the Bell-CHSH inequality.